Tendon anchorage and construction method of a pre-stressed concrete structure

ABSTRACT

An anchorage includes a bearing plate arranged in an end portion of a concrete structure with an insertion hole formed therein and formed with a through hole connecting to the insertion hole. A sleeve is inserted through the insertion hole and the through hole, with one end portion of the sleeve disposed on the outside of the structure. A tendon is inserted within the sleeve, with one end portion of the tendon disposed on the outside of the structure. A locknut is engaged with the one end portion of the sleeve and in contact with the outer surface of the bearing plate. A PC grout fills the insertion hole and the sleeve. Before filling, the tendon is applied with tension and, after strength expression of the PC grout, the tension is released. The tendon undergoes a Poisson effect to expand radially outward and compression stress occurs in the PC grout.

CROSS REFERENCE TO RELATED APPLICATION

This U.S. Patent Application claims the benefit of and priority to JPPatent Application 2020-172522 filed on Oct. 13, 2020, the entiredisclosure of the application being considered part of the disclosure ofthis application and hereby incorporated by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to a tendon anchorage and a constructionmethod of a pre-stressed concrete structure. The tendon anchorageaccording to the present invention is applicable to both a pre-stressedconcrete structure fabricated (constructed) using a post-tensioningsystem and a pre-stressed concrete structure fabricated using apre-tensioning system.

2. Background Art

Applying a continuous fiber-reinforced polymer strand as a tendon for apre-stressed concrete structure has conventionally brought moreadvantages than adapting a related-art PC steel strand as a tendon. Themost important advantage is that the continuous fiber-reinforced polymerstrand cannot get rusted and can be less likely to be deteriorated evenunder a rigorous environment. In addition, among continuousfiber-reinforced polymer strands, a continuous carbon fiber-reinforcedpolymer strand has an ultimate tensile stress of about 3600 N/mm², whilea PC steel strand has an ultimate tensile stress of about 1300 N/mm²,the former having a tensile strength about 2.8 times higher than that ofthe latter. Further, the continuous carbon fiber-reinforced polymerstrand has a material weight per unit ultimate load and per unit lengthof 0.76 g/m/kN, while the PC steel strand has of 4.23 g/m/kN, provingthat the former is about 1/5.6 lighter than the latter. Accordingly, thecontinuous carbon fiber-reinforced polymer strand with a smallercross-sectional area than a PC steel strand can be arranged uponintroducing pre-stress into concrete and also can be worked with reducedconstruction time and effort.

In terms of maintaining durability of a pre-stressed concrete structure,recent facilities have been planned to evaluate a life cycle costincluding not only an initial construction cost of a concrete structurebut also a maintenance cost. In this context, there has been a trend inwhich applying a continuous carbon fiber-reinforced polymer strand as atendon is also put in perspective of considerations.

However, to apply a continuous fiber-reinforced polymer strand as amajor tendon, there have been problems to be solved. One of the problemsrelates to an anchorage system of a continuous fiber-reinforced polymerstrand applied as a tendon. There has conventionally been employed aconstruction method in which with a steel wedge and an anchor head, a PCsteel strand is gripped directly at its any position and introduced witha tensioning force using a tensioning jack and/or anchored to a bearingplate via the anchor head. The most important advantage of thisconstruction method is its technical superiority in, for example, thatthe steel wedge can be used for gripping and releasing the PC steelstrand at its any position and that the steel wedge and the anchor headcan introduce, as a small-sized arrangement, a strong tensioning forceinto the pre-stressed concrete structure, thus having made a greatcontribution in working a pre-stressed concrete structure with a PCsteel strand applied thereto.

That is, the combination of a PC steel strand and a steel wedge causesthe surface of the steel wedge in a portion in contact with the PC steelstrand to be processed in a concavo-convex manner to bite the surface ofthe PC steel strand due to its wedge effect, whereby the PC steel strandand the steel wedge can be kept in a gripped state for transmission of atensioning force to the anchor head.

On the other hand, it is not possible to apply a steel wedge and ananchor head, which are applied to a PC steel strand, directly as ananchorage for a continuous fiber-reinforced polymer strand, which hassuperior characteristics as a tendon. When a steel wedge equivalent toone applied to a PC steel strand is applied to a continuousfiber-reinforced polymer strand, the surface of the steel wedge can bitethe surface of the continuous fiber-reinforced polymer strand due to itswedge effect, but no shear resistance is expected in the bitten portionof the continuous fiber-reinforced polymer strand. This cannot beapplied as an anchorage because, for example, the surface of thecontinuous fiber-reinforced polymer strand is extremely soft and may beeasily scraped off in the bitten portion or, if the wedge bites a largerportion, the continuous fiber-reinforced polymer strand may be cut off,whereby no gripping effect is expected.

The following two types of anchoring structural techniques are currentlyand practically implemented as anchorages for the continuousfiber-reinforced polymer strand. One of the anchoring structures employsa system in which a buffer material is wound around the continuousfiber-reinforced polymer strand and a wedge is applied thereon. A steelwedge is applied, though having a length greater than a steel wedge fora PC steel strand to adjust the wedge taper angle and requiring to use adedicated jack for push-in to the anchor head, placing limitingconditions to work. This is therefore used as a connection jig between apre-tensioning PC steel strand and a continuous fiber-reinforced polymerstrand because it cannot be applied for a post-tensioning tendon.

An anchorage of an expansion agent filling type fabricated by filling asteel pipe sleeve with expansion agent has successfully been employed toapply a continuous fiber-reinforced polymer strand as a post-tensioningtendon. The basic principle of this anchorage is to utilize thecontinuous fiber-reinforced polymer strand and the expansion-compressionstress of the expansion agent filling the steel pipe sleeve to increasethe shear resistance between the continuous fiber-reinforced polymerstrand and the steel pipe sleeve. This anchoring system can be appliedto both fixed end anchorage and tension stressing end anchorage in caseof a post-tension work. It is, however, necessary to control temperatureand humidity for the strength and the expansion check after filling ofthe expansion agent, which requires factory production. Upon shipmentfrom the factory, the length of the continuous fiber-reinforced polymerstrand and the anchoring position of the expansion agent-type anchorageare fixed.

Japanese Patent Application Publication No. H9-53325 disclosesconnection and traction with a related-art large-sized connecting memberto solve a problem of increase in the injection of mortar. That is,synthetic resin material or anchoring expansion material to be curedwithin a socket is injected into an intermediate portion of a fibercomposite strand to provide an anchoring body that is integrated withthe fiber composite strand via thus cured synthetic resin material oranchoring expansion material and, after tensioning, to be anchored to astructure through the intermediate anchoring body.

It is publicly known that a method of injection synthetic resin materialor anchoring expansion material into a clearance gap between a socketand a fiber composite strand can provide a structure of an anchoringbody. While the method disclosed in Japanese Patent ApplicationPublication No. H9-53325 requires the intermediate anchoring body to belocalized and place before tensioning, actual tensioning operationsundergo a change in the stretch of the fiber composite strand due totensioning because the length of the structure is different from that inthe design drawing and/or various frictional resistances occur duringtensioning. Accordingly, the invention of Japanese Patent ApplicationPublication No. H9-53325 is not practical in that it is necessary topre-install the intermediate anchoring body.

Japanese Patent Application Publication No. 2005-76388 discloses a fixedend anchorage for a high-strength fiber composite cable to beprocessable not in factory but on site, in which a collapsible bufferpartitioning material with through holes for expansive filling materialto pass therethrough and for a cable to be inserted therethrough isprovided in an intermediate portion of a sleeve to equalize theexpansion pressure of the expansive filling material in the lengthdirection. However, the theoretical development in Japanese PatentApplication Publication No. 2005-76388 comes under some questions. Oneof the questions resides in the description “This requires an expansionpressure of 50 MPa or higher, . . . requiring installation andtemperature control.” described in paragraph [0017].Expansion/compression stress by the expansive material occurs only ifexpansive strain resides within the expansion material and the innerdiameter, thickness, and elastic coefficient of a sleeve in which theexpansive strain is confined is determined. Extremely speaking, noexpansion pressure occurs in the expansive material unless there is asleeve or some other confining means.

There is a similar description in paragraph [0019] “According to anexperiment, it was proven that under a condition of natural cure, anexpansion pressure of 30 MPa could be achieved with a void of a size oneto three times the cross-sectional area of a cable”. Also, thedescription does not indicate, under a natural condition (on-site cure),how the expansive strain of the expansion material is, but only that theexpansion pressure is 30 MPa. The description “one to three times thecross-sectional area of a cable” only indicates information about theinner diameter of the sleeve in which the expansive strain is confined,without information about the thickness and elastic coefficient of thesleeve and the expansive strain of the expansion material, resulting ina lack of theoretical consistency.

International Publication No. WO 2011/019075 discloses a carbon fiberreinforced plastic cable covered with a frictional sheet with abrasiveparticles adhering thereto and a steel blade net tube thereon to allowfor wedge anchoring. An anchorage obtained by combining a sleeve and anexpansive material, which has conventionally been practiced as ananchorage for a continuous fiber-reinforced polymer strand, is fixed inits position because of being predicated on factory production. Thissystem suffers from no problem as an anchoring body for tensioning at afixed end anchorage. It is, however, difficult to apply this system to atension stressing end anchorage because such an anchorage as fabricatedpreliminarily in a factory fluctuates in its position. In the inventionof WO 2011/019075, since the frictional sheet and the blade net can bewound at any position to place a wedge, it is possible to set anyposition for tensioning by a tensioning jack. However, a steel wedge,which is applied to a PC steel strand, can practically grip the PC steelstrand at any position. On the other hand, in the method disclosed in WO2011/019075, portions reinforced by the frictional sheet and the steelblade net tube can only be gripped. Further, in order for the wedge togrip the continuous fiber-reinforced polymer strand with the frictionalsheet and the blade net wound therearound, another support by a wedgepush-in jack is also required, which causes a substantial problem in atensioning operation using a tensioning jack. It is therefore difficultto apply the method disclosed in WO 2011/019075 to an anchoring body ata tension stressing end anchorage. This technique is directed topre-tensioning and utilized as a connection jig between a continuousfiber-reinforced polymer strand and a related-art PC steel strandinstalled at a tension stressing end anchorage.

The system for introducing pre-stress into a concrete structure using atensioning force in a PC steel strand includes a post-tensioning systemand a pre-tensioning system. The tension introducing system that appliesa continuous fiber-reinforced polymer strand also includes apost-tensioning system and a pre-tensioning system. For each of thesystems, problems in a related-art system utilizing a continuousfiber-reinforced polymer strand will be provided below.

Post-Tensioning System

(1) Anchoring of Bearing Plate and Expansion Material Sleeve withLocknut

In the currently best-applied method of anchoring a continuousfiber-reinforced polymer strand, the clearance gap between thecontinuous fiber-reinforced polymer strand and a sleeve is filled withexpansion material (using cement-based expansion material) to utilizeexpansion/compression stress that occurs when the expansion materialexpands during its hydration process. The anchoring mechanism utilizesexpansion/compression stress between the continuous fiber-reinforcedpolymer strand and the sleeve to increase the contact compression stressagainst the distortional shear force acting between the outer surface ofthe continuous fiber-reinforced polymer strand and the inner surface ofthe sleeve for reliable anchoring of the continuous fiber-reinforcedpolymer strand within the sleeve.

The above-described method that applies an expansion material sleeve iscommonly and frequently employed in which after tensioning on thetensioning side, the tensioning force is anchored to the bearing plateprovided at an end portion of the concrete structure. In this method, alocknut is placed on the exterior of the expansion material sleeve toeventually transmit the tensioning force to the bearing plate. For thispurpose, the exterior of the sleeve is cut the screw so that the locknutcan work. A screw hole is also provided at the end portion of theexpansion material sleeve into which a screwed tension bar can beconnected to pull out the expansion material sleeve by tensioning jack.The expansion material sleeve is tensioned via the tension bar using acenter hole jack and, after reaching a predetermined tensioning force, alocknut preliminarily placed on the expansion material sleeve isfastened to the bearing plate so that the tensioning force istransmitted to the bearing plate and thereby tensioning stress occurs inthe concrete structure. The sheath is then filled with PC grout and theseries of tensioning operations ends with PC grout strength indication.

First Problem: the current method of anchoring a tensioning force to thebearing plate via the locknut on the expansion material sleeve puts alimitation on the length of the concrete structure to be tensioned. In acommon design rule, the tensioning force upon tensioning of thecontinuous fiber-reinforced polymer strand is set out to be 70% or lessof the guaranteed ultimate load capacity. That is, irrespective of thediameter of the continuous fiber-reinforced polymer strand used, thetensile strain of the continuous fiber-reinforced polymer strand upontensioning is 11,000μ to 12,000μ. If the tensioning member has a lengthof L=10 m, the deformation by tensioning is ΔL=110 mm to 120 mm. On theother hand, since the expansion material sleeve generally has a lengthof 300 to 400 mm at the longest, the continuous fiber-reinforced polymerstrand has a length of about 15 m to 20 m at the longest, in view of thehandling during anchoring.

Second Problem: the expansion material sleeve onto which the locknut isplaced generally has an outer diameter greater than the tube diameter ofthe sheath. Accordingly, at the start of tensioning, the end portion ofthe expansion material sleeve near the bearing plate is on the outsideof the bearing plate. This causes the expansion material sleeve toprotrude 300 to 400 mm from the tensioning end portion when the locknutis fixed to the bearing plate after tensioning. Also, in related-artanchoring of a PC steel strand at an end portion, the anchor head mayprotrude from the end portion. It is generally not desirable for amember playing a critical role in tensioning control to protrudesignificantly from the tensioning end anchorage portion. It is naturallynecessary to be equipped with a covering arrangement for management.

Third Problem: the expansion material sleeve is commercialized by beingfilled with expansive cement-based material to control expansion duringhydration. This requires quality control such as temperature andhumidity control in factory, so that factory production is only allowed.The structure into which pre-stress is introduced utilizing a tensioningforce in a tendon is a concrete structure and, if it is, for example, abridge, generally has a length of 30 m to 50 m, and an error of 0.5%occurring in the length direction can result in an error of 150 mm to250 mm in total length. Additionally, a pre-cast concrete, if joined,has a very high product accuracy, while the joint portion is operatedon-site and may have an accumulative error. In view of such a case wherean error may occur in the length of an intended structure into whichpre-stress is introduced, it is difficult to produce an expansionmaterial sleeve in a factory in advance. It is noted that a related-artPC steel strand cannot suffer from such a problem as described abovebecause it basically undergoes wedge anchoring and therefore the tendonis cut on-site as well as the anchoring may be made at any position.

(2) Method Without Tension Stressing End Anchorage in Post-TensioningSystem

This is not implemented in a post-tensioning system for anchoring acommon PC steel strand, but employed in a tendon system using acontinuous fiber-reinforced polymer strand, in which a sheath tube isfilled with PC grout with a tensioning force held after tensionstressing and, after PC grout strength indication, the tensioning forceof the tendon of the continuous fiber-reinforced polymer strand isreleased. This concept is based on the method of generation of atensioning force in the pre-tensioning system. In the pre-tensioningsystem, concrete is placed with a tensioning force in a tendon held and,after the concrete strength indication, the tendon is released tointroduce pre-stress into the concrete structure. In this case, when thetensioning force in the PC steel strand is released, the tensile strainacting on the PC steel strand in the axial direction (longitudinaldirection) undergoes a Poisson effect, and expansive strain occurs inthe diameter direction (lateral direction) of the tendon. In comparison,since the concrete placed around the PC steel strand serves as aconfining material, compression stress occurs between the surface of thePC steel strand and the concrete as a reaction force against theconfinement effect, resulting in an increase in the shear or bondresistance for slipping between the concrete and the PC steel strand.

Also, in a post-tensioning system using a continuous fiber-reinforcedpolymer strand, since PC grout filling the interior of the sheath tubeserves as a confining material, when the tensioning force is released,confining compression stress occurs on the surface of the continuousfiber-reinforced polymer strand, resulting in an increase in the shearresistance. In the post-tensioning system using a related-art PC steelstrand, a method of releasing a tip end of the PC steel strand withouttension anchoring using a bearing plate and/or an anchor head is notemployed for the reason that the surface of the PC steel strand issmooth and has a poor adhesive characteristic with PC grout. On theother hand, the continuous fiber-reinforced polymer strand is lesslikely to be adhered with PC grout than a rebar, but more likely than aPC steel strand.

First Problem: after tension introduction, no tensioning force istransmitted via a locknut to a bearing plate, so that no pre-stressoccurs in the concrete in the vicinity of the tensioning end portion.Even when the above-described Poisson effect may cause a shearresistance to work between the continuous fiber-reinforced polymerstrand and the PC grout, no pre-stress is expected within the range of50φ to 60φ from the tension stressing end portion (φ represents thediameter of the continuous fiber-reinforced polymer strand). It istherefore difficult to apply this method when pre-stress is required upto around the end portion of the concrete structure.

Second Problem: the first problem above specifically means that it isdifficult to introduce tensioning stress into a small-sized concretestructure. Specifically, when a continuous fiber-reinforced polymerstrand of, for example, φ=15.2 mm is used, the range within whichsufficient tensioning stress is not expected is 60φ=912 mm. Theabove-described anchoring method cannot be applied to a structure havinga length of, for example, 3 m to 4 m.

Pre-Tensioning System

The mechanism of tensioning stress introduction in a pre-tensioningsystem is as described above. Accordingly, even when a continuousfiber-reinforced polymer strand may be used as a tendon, if concreteplaced after tensioning reaches a predetermined strength and introducestensioning stress, there is a problem that the vicinity of the tensionstressing end portion (at a distance of 50φ to 60φ) is not introducedwith tensioning stress. It is therefore difficult to introducepre-stress into a short member in a pre-tensioning system, including thecase of a pre-tensioning system using a related-art PC steel strand.

PC steel strands have conventionally been applied frequently as tendons.The advantage of PC steel strands is that with a steel wedge and ananchor head, a PC steel strand is gripped directly at its any positionand introduced with a tensioning force using a tensioning jack and/oranchored to a bearing plate via the anchor head, whereby pre-stress canbe introduced up to around the tensioning end portion.

On the other hand, a continuous fiber-reinforced polymer strand to whichthe present invention is directed is formed by processing polymerstrands of, for example, carbon fiber, aramid fiber, glass fiber, or thelike into a rope. Such a continuous fiber-reinforced polymer strand thushas reduced lateral rigidity and/or strength and cannot be anchored witha steel wedge as before.

Accordingly, an anchoring method that utilizes expansion/compressionstress of an expansion material filling the clearance gap between asleeve and a continuous fiber-reinforced polymer strand and cured thereis currently applied most frequently for anchoring of a continuousfiber-reinforced polymer strand and in widespread use as a practicalmethod.

Another anchoring method is also applied in which a continuousfiber-reinforced polymer strand is reinforced with a friction enhancingsheet and a steel blade net tube therearound and, on the outsidethereof, applied with a steel wedge having a wedge angle looser thanthat of a related-art steel wedge. However, this method is limited inits manner of operation and therefore has problems to be applied at thetension stressing end portion.

SUMMARY OF THE INVENTION

In view of the current situations above, it is an object of the presentinvention to provide an anchorage with neither site-operationallimitation nor working cost increase, including a simple anchoringmechanism and a structure in which a sleeve, a locknut, and a bearingplate can be designed with common structural computation.

It is another object of the present invention to anchor a tendonreliably to a concrete structure to efficiently introduce pre-stressinto the concrete structure.

The present invention provides a tendon anchorage in a concretestructure into which pre-stress is introduced using a post-tensioningsystem. The tendon anchorage according to a first aspect of theinvention includes a bearing plate arranged in an outer end portion of aconcrete structure with an insertion hole formed therein and formed witha through hole connecting to the insertion hole of the concretestructure, a hollow sleeve inserted through the insertion hole of theconcrete structure and the through hole of the bearing plate, one endportion of the sleeve put on the outside of the concrete structure, atendon inserted within the sleeve, one end portion of the tendonanchored to the concrete structure and the other end portion of thetendon put on the outside of the concrete structure, a locknut engagedwith the other end portion of the sleeve, which is put on the outside ofthe concrete structure, and in contact with the outer surface of thebearing plate, and PC grout filling the insertion hole and the sleeve,in which before filling with the PC grout, the other end portion of thetendon is pulled outward by a tensioning device with the one end portionbeing fixed so that the tendon is applied with tension and, afterexpression of a predetermined strength in the PC grout, the tension isreleased by the tensioning device, and the tendon undergoes a Poissoneffect to expand radially outward and compression stress occurs in thePC grout between the expanding tendon and the sleeve.

One end portion (fixed end anchorage) of the tendon is fixed to theconcrete structure and the other end portion (tension stressing endanchorage) of the tendon is pulled outward by the tensioning device. Theone end portion of the tendon may be anchored by a fixing device on theoutside of the concrete structure or may be anchored to the concretestructure using, for example, PC grout within the insertion hole.

The present invention also provides a tendon anchorage in a concretestructure into which pre-stress is introduced using a pre-tensioningsystem. The tendon anchorage according to a second aspect of theinvention includes a pair of locknut-and-bearing-plates arranged,respectively, in the end portions within a concrete structure and eachformed with a through hole, a hollow sleeve engaged with each of thepair of locknut-and-bearing-plates and connecting to the through holes,a tendon inserted through the through hole of each of thelocknut-and-bearing-plates in the end portions within the concretestructure and the hollow sleeve, the end portions of the tendon put onthe outside of the concrete structure, and PC grout filling the sleeve,in which before the PC grout filling the sleeve and concrete forming theconcrete structure being placed, with one end portion of the tendonbeing fixed using a fixing device, the other end portion of the tendonis pulled outward by a tensioning device so that the tendon is appliedwith tension and, after expression of a predetermined strength in the PCgrout and the concrete, the tension is released by the tensioningdevice, and the tendon undergoes a Poisson effect to expand radiallyoutward and compression stress occurs in the PC grout between theexpanding tendon and the sleeve.

The tendon preferably employs a continuous fiber-reinforced polymerstrand. The continuous fiber-reinforced polymer strand is formed bybundling several tens of thousands of continuous carbon fibers, aramidfibers, glass fibers, or the like and impregnating with thermosettingresin such as epoxy resin or vinyl ester resin or thermoplastic resinsuch as polycarbonate or polyvinyl chloride for curing. The continuousfiber-reinforced polymer strand may be formed by bundling severalcontinuous fibers and twisting several continuous fiber bundles.

Preferably, a hollow sheath tube is embedded in the concrete structure,and the hollow space of the sheath tube is used as the insertion hole.

In accordance with the present invention, the Poisson effect causes thetendon to expand radially outward and thereby compression stress occursin the PC grout between the tendon and the surrounding sleeve, wherebythe tendon is confined reliably within the sleeve and anchored over theentire periphery within the range surrounded by the sleeve.

The tendon also contracts in the longitudinal direction (acts to recoverits original length) when the tension is released. Since the locknut orthe locknut-and-bearing-plates are engaged with one end portion of thesleeve that is anchored reliably with the tendon, when the tensionwithin the tendon is released and the tendon contracts in thelongitudinal direction, the locknut engaged with the one end portion ofthe sleeve that is anchored reliably with the tendon is urged againstthe bearing plate (post-tensioning system) or thelocknut-and-bearing-plates in the end portions within the concretestructure are applied with a force that causes them to come close toeach other (pre-tensioning system), whereby pre-stress can be introducedefficiently into the concrete structure.

Principle of Anchoring According to the Invention

A tendon anchoring mechanism according to the present invention will bebriefly described. When the tendon is applied with tension, tensilestrain occurs within the tendon in the tensioning direction (in thelongitudinal direction of the tendon) and, at the same time, a Poissoneffect causes compressive strain to occur in the circumferentialdirection of the tendon, which is orthogonal to the tensioningdirection. With this state being maintained, PC grout fills theclearance gap between the sleeve and the tendon. The PC grout is thencured for expression of a predetermined strength. After strengthexpression of the PC grout, when the tension within the tendon isreleased (the tensioning force is released), the circumferentialcompressive strain existing in the tendon is released. When thecompressive strain within the tendon is released, the tendon expandsradially outward (Poisson effect, Poisson phenomenon). Compressionstress occurs in the PC grout between the expanding tendon and thesleeve, whereby the tendon and the sleeve are tightly anchored to eachother.

The locknut engaged with the anchored sleeve shares a tensioningreaction force, which is introduced via the bearing plate provided in anend portion of the concrete structure into the concrete structure aspre-stress effective over the entire length also including the endportion of the concrete structure.

It has practically been proven based on the performance of expansionmaterial filling sleeves that when compression stress occurs in PC groutpresent in the clearance gap between a tendon and a sleeve, an anchoringmechanism occurs between the tendon and the sleeve. Whether or not theforegoing theoretical development is correct will hereinafter beconsidered quantitatively by calculating compression stress occurring inPC grout when a continuous carbon fiber-reinforced polymer strand isused as a tendon.

Compression Stress Occurring in PC Grout According to the Invention

The anchoring mechanism will be described by specifically calculatingcompression stress occurring in PC grout for a continuous carbonfiber-reinforced polymer strand that is formed by applying carbon fiberas a continuous fiber-reinforced polymer strand. The shape andcharacteristics of the subject continuous carbon fiber-reinforcedpolymer strand (hereinafter referred to as CFCC (Carbon Fiber CompositeCable) which is a product name) and the sleeve are as follows.

1) Data on CFCC

The diameter of CFCC φ=17.2 mm, effective cross-sectional area of CFCCAcf=151.1 mm², elastic coefficient of CFCC Ecf=150 kN/mm², guaranteedultimate load of CFCC Pu=385 kN, Poisson's ratio of CFCC v=0.06 (fromcarbon fiber reinforced plastic test data by Shimadzu Corporation).

2) Data on Sleeve

The material of the sleeve is STKM13A, inner radius of the sleeve R=11.4mm, thickness t=4.5 mm, elastic coefficient of the sleeve E=210 kN/mm².

The maximum tensioning force that can be applied to CFCC when appliedwith tension is specified 70% or less of the guaranteed ultimate load ofCFCC. Accordingly, the tensile strain during tensioningεu=0.7×Pu/(Acf×Ecf)=11,890μ.

When the tension within CFCC is released, a Poisson effect causeslateral (circumferential) expansive strain to occur in CFCC inproportion to the Poisson's ratio and thereby CFCC to have an increaseddiameter. The expansive strain εlu=v×εu=713μ, where εlu represents thelateral expansive strain. Accordingly, the expansion of the inner radiusR within the sleeve ΔR=φ/2×εlu=6,132×10⁻⁶ mm when a Poisson effectoccurs in CFCC from which the tension is released and, as a result, CFCCexpands.

When the inner radius within the sleeve expands by the length ΔR,applying a theoretical solution of “Theoretical Analysis of InnerPressure Acting on Thin-walled Ring”, the compression stress p occurringin the PC grout can be solved as p=ΔR×t×E/R2=44.6 MPa.

The relationship between an increase in the compression stress of the PCgrout and anchoring of CFCC to the sleeve via the PC grout willhereinafter be described. The performance of anchoring is determined bya combination for minimum resistance among shear fracture stress of thePC grout itself between CFCC and the sleeve, frictional force andadhesion acting at the interface between the PC grout and CFCC, andfrictional force and adhesion acting at the interface between the PCgrout and the interior of the sleeve.

First, as for resistive shear stress of the PC grout itself, since thePC grout is very thin in a state where compression stress acts thereon,shear fracture cannot occur. On the other hand, in comparison betweenthe interface between the PC grout and CFCC and the interface betweenthe PC grout and the interior of the sleeve, the former has a resistancearea smaller than that of the latter and is likely to have a reducedfrictional force, while the interface between the PC grout and CFCC islikely to have increased adhesive stress. In contrast, the latter has areverse of the relationship above. In any event, shear force acting atthe interface with the PC grout is dominated mainly by resistance due toa frictional force, which is derived mainly from compression stress ofthe PC grout. Since frictional resistance stress is represented by theproduct of friction coefficient and compression stress acting at theinterface, it is advantageous that the PC grout have high compressionstress p.

Compression Stress Occurring in Expansion Material of Related-ArtExpansion Material Filling Sleeve

Naturally, a Poisson effect cannot be applied to a related-art expansionmaterial filling sleeve as in the present invention. However, theeventual anchoring mechanism uses, in lieu of PC grout, expansive filler(expansive cement grout) obtained by containing expansive material andutilizes expansion/compression stress that occurs when the groutmaterial expands during its hydration process, which is consequently thesame as the mechanism applied upon usage as an anchoring device.

Upon evaluation of appropriateness of the present invention, thecompression stress p occurring in an expansion material filling sleeve,which has already been put into practice, is utilized to provisionallycalculate the expansion material compression stress p occurring with thesame shape and material of a CFCC tendon and a sleeve as in the presentinvention.

1) Data on CFCC

The diameter of CFCC φ=17.2 mm, effective cross-sectional area of CFCCAcf=151.1 mm², elastic coefficient of CFCC Ecf=150 kN/mm², guaranteedultimate load of CFCC Pu=385 kN, Poisson's ratio of CFCC v=0.06.

2) Expansive filling Material

Expansive strain εe=600μ (strain in an unconfined state under acontrolled curing temperature condition)

3) Data on Sleeve

The material of the sleeve is STKM13A, inner radius of the sleeve R=11.4mm, thickness t=4.5 mm, elastic coefficient of the sleeve E=210 kN/mm².

The expansive grout fills the inner radius of the sleeve. There is aCFCC with a diameter φ of 17.2 mm at the center of the sleeve. Since theexpansive grout fills the space between the CFCC strands, the expansionmaterial may expand within the range of the inner radius of the sleeve.As a result, ΔR=εe×R=6,840×10⁻⁶ mm, where ΔR represents the expansion ofthe inner radius R of the sleeve.

When the inner radius within the sleeve expands by the length ΔR,applying a theoretical solution of “Theoretical Analysis of InnerPressure Acting on Thin-walled Ring”, the compression stress p occurringin the expansive grout can be solved as p=ΔR×t×E/R2=49.7 MPa.

As described heretofore, the compression stress occurring in the PCgrout according to the present invention is approximately equal to thecompression stress occurring in the expansive grout within therelated-art expansive sleeve, which theoretically validates theanchoring effect according to the present invention.

Elements required for the anchorage according to the present inventionto come into effect are a bearing plate arranged in an end portion of aconcrete structure, a tendon, a sleeve, a locknut engaged with an endportion of the sleeve, and PC grout. These elements do not requirespecially advanced processing. Machine processing is required only forscrew fixation processing of the locknut to the end portion of thesleeve and hole drilling into the bearing plate. The PC grout may employthe same material as that filling the sheath tube after tensioning in acommon pre-tensioning system. Also, as for filling with the PC grout, arelated-art grout filling technique may be used for the PC grout tosufficiently fill the clearance gap between the continuousfiber-reinforced polymer strand and the sleeve.

In accordance with the anchoring mechanism according to the presentinvention, it was proven, from a result of the provisional calculationfor the same sleeve shape and continuous fiber-reinforced polymerstrand, that the compression stress occurring in the PC grout accordingto the present invention is equal to that within the expansive sleeve.

The finished product as an anchoring device has many advantages in, forexample, working process, easy workmanship, time and effort for qualitycontrol, anchoring effect, working cost, performance as worked product.

In an implementation, the compression stress p occurring in the PC groutand calculated by the following equation 1 is 20 to 60 MPa:p=φ/2×v×(0.7×εu)×(t×E)/(R×R) (Eq.1), where φ, v, εu, R, t, and Erepresent, respectively, the diameter of the tendon, Poisson's ratio ofthe tendon, tensile strain with guaranteed ultimate load of the tendon,inner radius of the sleeve, thickness of the sleeve, and elasticcoefficient of the sleeve.

Among factors that may contribute to anchoring performance, ones indirect relation with the anchoring mechanism is selected, and the rangeof compression stress acting on the PC grout material, which is obtainedfrom a simple calculation using data of the factors, is shown toindicate a quantitative criterion for determining the anchoringperformance. That is, in the present invention, the quantitative rangewithin which superior anchoring performance can be delivered is 20 to 60MPa in a combination of components to be applied.

The inner surface of the sleeve is preferably made concavo-convex. Forexample, the inner surface of the sleeve may be threaded to be madeconcavo-convex. As mentioned above, compression stress occurring in thePC grout is transmitted mutually as shear stress between the interior ofthe sleeve and the PC grout. Since the shear stress is obtained bymultiplying compression stress acting within the sleeve by the frictioncoefficient, the concavo-convex inner surface of the sleeve contributesto an increase in the friction coefficient.

The outer surface of the sleeve is also preferably made concavo-convex.Resistance due to adhesive stress occurs between the exterior of thesleeve and the PC grout in contact with the exterior of the sleeve.Since the resistance is transmitted to the locknut engaged with thesleeve, the concavo-convex outer surface of the sleeve contributes to anincrease in the adhesive stress.

In another implementation, the bearing plate arranged in the end portionof the concrete structure consists of a single continuous plate. Thebearing plate, when arranged in the end portion of the concretestructure consists of a single continuous plate, can play a role as abearing plate in a power transmission tower foundation as well as offixing tower foundation truss to transmit a cross-sectional force actingon the tower foundation truss to the concrete foundation.

Preferably, multiple convex shear keys are provided on a surface of thebearing plate opposed to the concrete structure, and recesses that theshear keys enter are formed in positions corresponding to those of theshear keys on a surface of the concrete structure opposed to the bearingplate. The shear keys are provided to efficiently and economicallyresist a horizontal force acting on the base plate of the foundation,whereby even such a little addition can look for major shear resistanceeffects.

In an implementation, the locknut and the bearing plate are formedintegrally. It is therefore possible to fabricate a pre-tensioned memberwith a small dimension.

In another implementation, the sleeve is formed with a filling hole forthe PC grout to fill the sleeve and an air discharge hole for air to bedischarged. The PC grout can fill the sleeve reliably.

The present invention also provides a construction method of apre-stressed concrete structure using a post-tensioning system. Themethod includes arranging, in an end portion of a concrete structurewith an insertion hole formed therein, a bearing plate with a throughhole connecting to the insertion hole of the concrete structure,engaging a locknut with one end portion of a hollow sleeve, insertingthe sleeve through the through hole of the bearing plate into theinsertion hole of the concrete structure and placing the locknut engagedwith the one end portion of the sleeve on the bearing plate, inserting atendon into the sleeve, fixing one end portion of the tendon to theconcrete structure, placing a tensioning device in the other end portionof the tendon, with the tendon being applied with tension, filling theinsertion hole of the concrete structure with PC grout such that the PCgrout also fills the clearance gap between the sleeve and the tendoninserted into the sleeve, and after the PC grout reaching apredetermined strength, releasing the tension within the tendon.

The present invention further provides a construction method of apre-stressed concrete structure using a pre-tensioning system. Themethod includes providing a formwork, installing, in each lateral endportion within the formwork, a hollow sleeve and alocknut-and-bearing-plate engaged with the sleeve such that thelocknut-and-bearing-plate comes into contact with each lateral endportion within the formwork, inserting a tendon through installationholes formed in the lateral end portions of the formwork into theformwork and putting the end portions of the tendon out through therespective lateral end portions of the formwork, while within theformwork, inserting the tendon into the sleeve installed in each lateralend portion within the formwork, placing a fixing device in one endportion of the tendon put out of the formwork through one lateral endportion of the formwork, placing a tensioning device in the other endportion of the tendon put out of the formwork through the other lateralend portion of the formwork, applying the other end portion of thetendon with tension using the tensioning device, with the tendon beingapplied with the tension, filling the sleeve in each lateral end portionwithin the formwork with PC grout, placing concrete within the formwork,and after the PC grout and the concrete reaching a predeterminedstrength, releasing the tension within the tendon.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view showing how pre-stress is introducedinto a concrete structure using a post-tensioning system.

FIG. 2 is a cross-sectional view showing how pre-stress is introducedinto a concrete structure using a post-tensioning system.

FIG. 3A is an enlarged cross-sectional view showing a tendon in atensioned state together with a surrounding sleeve and PC grout fillingthe sleeve.

FIG. 3B is an enlarged cross-sectional view showing a tendon in atension-released state together with the surrounding sleeve and the PCgrout filling the sleeve.

FIG. 4 is a cross-sectional view of a first example showing howpre-stress is introduced into a concrete structure using apost-tensioning system.

FIG. 5 is a cross-sectional view of a second example showing howpre-stress is introduced into a concrete foundation structure using apost-tensioning system.

FIG. 6 is a cross-sectional view of a third example showing howpre-stress is introduced into a PC composite bridge using apost-tensioning system.

FIG. 7 shows a process of manufacturing a pre-stressed concretestructure member using a pre-tensioning system.

FIG. 8 shows a process of manufacturing a pre-stressed concretestructure member using a pre-tensioning system.

FIG. 9 shows a process of manufacturing a pre-stressed concretestructure member using a pre-tensioning system.

FIG. 10 is a partially enlarged plan view showing an enlarged version ofone end portion of the concrete structure member shown in FIG. 8.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIGS. 1 and 2 are cross-sectional views showing how pre-stress isintroduced into a concrete structure using a post-tensioning system. Aconcrete structure introduced with pre-stress is called pre-stressedconcrete structure. FIG. 3A is an enlarged schematic cross-sectionalview showing a tendon (a stressing member, a tensioning member) in atensioned state to be described below together with a surrounding sleeveand PC grout filling the sleeve. FIG. 3B is an enlarged schematiccross-sectional view showing a tendon in a tension-released statetogether with the surrounding sleeve and the PC grout filling the sleeveas well as compression stress (double-headed arrows) occurring in the PCgrout.

As will be described in more detail below, the tendon is provided withinthe concrete structure to introduce pre-stress into the concretestructure. When one end (fixing end) of the tendon is fixed and theother end (tensioning end) is pulled outward, the tendon is applied withlongitudinal tension. A fixing device for fixing one end of the tendonis shown schematically in FIGS. 1 and 2. A tensioning device for pullingthe other end of the tendon is not shown in FIGS. 1 and 2. Specificexamples of the fixing device and the tensioning device will hereinafterbe described.

Referring to FIG. 1, a metal or polyethylene cylindrical sheath tube 5is embedded in the concrete structure 2. The hollow space of the sheathtube 5 is used as an insertion hole 4 through which a sleeve 7 to bedescribed below is inserted. The sheath tube 5 may employ, for example,a spiral sheath with its inner and outer peripheral surfaces madeconcavo-convex.

A metal bearing plate 3 is provided on the upper surface of the concretestructure 2. The bearing plate 3 is formed with a cylindrical throughhole 3 a having a diameter approximately equal to the outer diameter ofthe sheath tube 5 provided in the concrete structure 2, and the sheathtube 5 is also inserted through the through hole 3 a of the bearingplate 3. The insertion hole 4 (hollow space of the sheath tube 5) isopened outward at the upper end face of the bearing plate 3. The throughhole 3 a of the bearing plate 3 may be formed to have a diameterslightly greater than the outer diameter of the sheath tube 5.

A metal cylindrical rigid sleeve 7 is inserted through the insertionhole 4. The sleeve 7 has an outer diameter smaller than the insertionhole 4 (inner diameter of the sheath tube 5). An annular clearance gapis formed between the sheath tube 5 and the sleeve 7 in across-sectional view. The inner and outer peripheral surfaces of thesleeve 7 may also be made concavo-convex (e.g., threaded). Both theinner and outer peripheral surfaces of the sleeve 7 are preferably madeconcavo-convex, though may be either the inner or outer peripheralsurface of the sleeve 7. For the sleeve 7, a metal member having arigidity in the circumferential direction tolerable the compressivestress 18 occurred in a PC grout 15 described later can be used. Therigidity of the sleeve 7 can be adjusted by the rigidity of the adoptedmetal member itself and the wall thickness thereof.

An upper end portion of the sleeve 7 extends above the bearing plate 3and a screw thread 11 is formed on the outer peripheral surface of theupper end portion of the sleeve 7 extending above the bearing plate 3. Alocknut 8 with a screw thread formed on the inner peripheral surfacethereof is threadably mounted on the upper end portion of the sleeve 7with the screw thread 11 formed on the outer peripheral surface thereofand engaged tightly with the outer peripheral surface of the sleeve 7 incontact with the upper surface of the bearing plate 3.

The tendon 1, which has a diameter smaller than the inner diameter ofthe sleeve 7, is inserted through the hollow space 6 of the sleeve 7extending from the locknut 8 through the bearing plate 3 into theconcrete structure 2. An annular clearance gap is also formed betweenthe tendon 1 and the inner peripheral surface of the sleeve 7 in across-sectional view.

The tendon 1 can employ a continuous fiber-reinforced polymer strandcomposed of one core strand and multiple (e.g., six) side strandstwisted around the core strand. The tendon 1 and the core strand and theside strands forming the tendon 1 each have an approximately circularshape in a cross-sectional view (not shown). Also, the core strand isarranged at the center of the tendon 1 and the multiple side strands arepositioned to surround the core strand in a cross-sectional view. Thetendon 1 has a diameter of about 5 mm to 40 mm, for example.

The core strand and the side strands constituting the tendon 1 each forma resin containing fiber bundle obtained by bundling, into across-sectionally circular shape, multiple (e.g., several tens ofthousands of) elongated continuous carbon fibers impregnated withthermosetting resin or thermoplastic resin for curing. Each of thecarbon fibers is very thin, having a diameter of 5 μm to 7 μm, forexample. The tendon 1 may be said to be made of Carbon Fiber ReinforcedPlastics. Aramid fiber or glass fiber may be used in lieu of carbonfiber. Epoxy resin or vinyl ester resin, for example, is used as thethermosetting resin. Polycarbonate or polyvinyl chloride, for example,is used as the thermoplastic resin.

One end (lower end in FIG. 1; fixing end) of the tendon 1 extendingdownward from the lower surface of the concrete structure 2 is fixed bya fixing device 12. The other end (upper end in FIG. 1; tensioning end)of the tendon 1 extending upward from the locknut 8 is pulled (alsoreferred to as “applied with tension”) upward by a tensioning device(not shown). Since the one end (fixing end) of the tendon 1 is fixed,when the other end (tensioning end) of the tendon 1 is pulled, alongitudinal tensile force (also referred to as tensioning force) isapplied to the tendon 1 and stress corresponding thereto occurs withinthe tendon 1. The tendon 1 stretches in proportion to the stress andcross-sectional contraction occurs (the diameter of the tendon 1contracts). In FIG. 3A, the tendon 1 (its thickness) before being pulledin the longitudinal direction is indicated by broken lines.

As shown in FIGS. 2 and 3A, PC grout 15 fills the sleeve 7 with thetendon 1 kept in a tensioned state. Referring to FIG. 2, the PC grout 15fills not only the sleeve 7 but also the sheath tube 5.

Referring to FIGS. 2 and 3B, after the PC grout 15 is cured and apredetermined strength is expressed, the tension within the tendon 1 bythe tensioning device is released. The tendon 1, when applied withtension by the tensioning device, stretches in the longitudinaldirection (axial direction) and thereby tensile strain occurs in thelongitudinal direction. When the tension within the tendon 1 isreleased, a Poisson effect occurs in the tendon 1 and expansive strainby the Poisson's ratio occurs circumferentially outward of the tendon 1(in the direction perpendicular to the axis), whereby the tendon 1expands circumferentially outward. That is, comparing FIGS. 3A and 3B,when the tension within the tendon 1 is released, the tendon 1 contractsin the longitudinal direction (L1>L2), while expands in the radialdirection (D1<D2). It is noted that how the tendon 1 contracts andexpands is drawn with considerable emphasis in FIGS. 3A and 3B. As aresult, as schematically shown in FIG. 3B, predetermined compressionstress 18 occurs in the PC grout 15 filling the clearance gap betweenthe tendon 1 and the sleeve 7. This compression stress 18 causes thetendon 1 to be anchored reliably to the sleeve 7. In addition, since thetension within the tendon 1 is released and the tendon 1 contracts inthe longitudinal direction, the locknut 8 threadably coupled to theupper end portion of the sleeve 7 is urged against the bearing plate 3(tensioning reaction force) and pre-stress occurs in the concretestructure 2. The tendon 1 is thus anchored reliably within the concretestructure 2 and the structural performance of the concrete structure 2is improved with the pre-stress introduced.

Specific examples of a concrete structure introduced with pre-stresswill hereinafter be described with reference to FIGS. 4 to 10.

FIRST EXAMPLE

FIG. 4 shows a first example, illustrating in detail examples of afixing device and a tensioning device for applying tension to a tendon.FIG. 4 does not show a sheath tube that is provided to allow aninsertion hole within the concrete structure.

Referring to the left part in FIG. 4, the fixing device includes abearing plate 23A provided at one end (left end in FIG. 4) of theconcrete structure 22, a locknut 28A, a ram chair 38, an anchor head 39,a friction sheet and blade net 41, and a wedge 40. A sleeve 27A isinserted through a sheath tube (insertion hole) that is embedded in theconcrete structure 22, and a tendon 21 is inserted through the sleeve27A. The sleeve 27A is inserted through the through hole of the bearingplate 23A, and a leading end portion thereof is put on the outside ofthe bearing plate 23A. The locknut 28A is threadably mounted on theleading end portion of the sleeve 27A that is put on the outside of thebearing plate 23A.

The ram chair 38 is installed on the bearing plate 23A in a mannersurrounding the locknut 28A. The ram chair 38 has an insertion hole atits center through which the tendon 21 is inserted, and a leading endportion (fixing end) of the tendon 21 is inserted through the insertionhole of the ram chair 38 and put on the outside of the ram chair 38.

The anchor head 39 is installed on the ram chair 38. The anchor head 39has an insertion hole through which the leading end portion of thetendon 21 is inserted and a hollow space tapered for wedge into whichthe wedge 40 is pushed. The leading end portion of the tendon 21 that isput on the outside of the ram chair 38 is inserted through the insertionhole and the hollow space of the anchor head 39 to extend out of theanchor head 39. The friction sheet and blade net 41 is wound around theleading end portion of the tendon 21 that is put on the outside of theanchor head 39 and the exterior thereof is covered with the wedge 40,and the leading end portion of the tendon 21 covered with the wedge 40is pushed into the hollow space of the anchor head 39. The leading endportion of the tendon 21 is anchored reliably within the hollow spacetapered for wedge of the anchor head 39.

The friction sheet and blade net 41 is put on the outer peripheralsurface of the leading end portion of the tendon 21 covered with thewedge 40 to reduce the clamping force of the wedge 40 against the tendon21.

Referring to the right part in FIG. 4, the tensioning device includes abearing plate 23B provided at the other end (right end in FIG. 4) of theconcrete structure 22, a locknut 28B, ram chairs 31, 32, a ring nut 33,an expansion material filling sleeve 34, a tension bar 35, a center holetensioning jack 36, a wedge 42, and an anchor head 43.

A sleeve 27B is inserted through an insertion hole of the concretestructure 22, and a tendon 21 is inserted through the sleeve 27B. Thesleeve 27B is inserted through the through hole of the bearing plate 23Band put on the outside of the bearing plate 23B. The locknut 28B isthreadably mounted on the leading end portion of the sleeve 27B that isput on the outside of the bearing plate 23B.

The first ram chair 31 is installed on the bearing plate 23B in a mannersurrounding the locknut 28B. The first ram chair 31 has an insertionhole at its center through which the tendon 21 is inserted, and aleading end portion (tensioning end) of the tendon 21 is insertedthrough the insertion hole of the first ram chair 31 and put on theoutside of the first ram chair 31.

The expansion material filling sleeve 34 is fabricated in a factory andprovided on the leading end portion of the tendon 21 that is put on theoutside of the first ram chair 31. Expansion material fills theexpansion material filling sleeve 34 and provides expansion pressure ofthe expansion material to anchor the expansion material filling sleeve34 reliably to the leading end portion of the tendon 21. The outerperipheral surface of the expansion material filling sleeve 34 isthreaded, through which the ring nut 33 is fixed to the expansionmaterial filling sleeve 34.

The second ram chair 32 is overlaid on the first ram chair 31 in amanner surrounding the ring nut 33 and the expansion material fillingsleeve 34. The second ram chair 32 also has an insertion hole at itscenter through which the tendon 21 is inserted, and a leading endportion (tensioning end) of the tendon 21 is inserted through theinsertion hole of the second ram chair 32 and put on the outside of thesecond ram chair 32.

The center hole tensioning jack 36 is installed on the second ram chair32. After the installation of the center hole tensioning jack 36, thetension bar 35 is engaged with the inner thread of the expansionmaterial filling sleeve 34. The leading end portion of the tendon 21passes through the center hole tensioning jack 36 to be anchored to theleading end of the ram of the center hole tensioning jack 36 using thewedge 42 and the anchor head 43. When the center hole tensioning jack 36is actuated and the tendon 21 is applied with tension, the center holetensioning jack 36 moves away from the second ram chair 32. Since thecenter hole tensioning jack 36 is connected with the above-describedexpansion material filling sleeve 34 by the tension bar 35, theexpansion material filling sleeve 34 also moves away from the first ramchair 31 by the tension bar 35. When a predetermined tensioning force isapplied to the tendon 21, the ring nut 33 that is placed on the outerperipheral surface of the expansion material filling sleeve 34 isfastened and thereby fixed and anchored to the first ram chair 31. Whenthe ring nut 33 is fastened, the tensioning force is maintained at thetensioning end by the first ram chair 31, the expansion material fillingsleeve 34, and the ring nut 33. Thereafter, the center hole tensioningjack 36 is de-actuated, the center hole tensioning jack 36, the tensionbar 35, and the second ram chair 32 can be uninstalled. The center holetensioning jack 36, the tension bar 35, and the second ram chair 32,after uninstalled, can be used to apply tension to a tendon 21 atanother location.

PC grout fills the insertion hole (sheath tube) of the concretestructure 22 with the tendon 21 kept in a tensioned state. The PC groutalso fills the sleeves 27A, 27B. Before filling with the PC grout, sealmay be applied around the bearing plates 23A, 23B so that the PC groutcannot leak out of the bearing plates 23A, 23B. After the PC grout iscured and a predetermined strength occurs, the tendon 21 is cut off inthe vicinity of the locknut 28A, 28B and thereby the tension isreleased. As described above, when the tensioning force is released,predetermined compression stress occurs in the PC grout filling theclearance gap between the tendon 21 and the sleeves 27A, 27B, and thecompression stress causes the tendon 21 to be anchored reliably to thesleeves 27A, 27B. In addition, tensioning stress is introduced into theconcrete structure 22 via the bearing plates 23A, 23B.

SECOND EXAMPLE

FIG. 5 is a cross-sectional view showing how pre-stress is introducedinto a concrete foundation structure using a post-tensioning system.Also in FIG. 5, a sheath tube is not shown. This presents an anchoringconstruction method that is hard to achieve with a related-art methodand can specifically be utilized, for example, as a construction methodfor efficiently and reasonably anchoring a steel tower portion of apower transmission tower foundation to a concrete foundation.

FIG. 5 is a vertical cross-sectional view of a portion of a columnar orrectangular concrete foundation structure 52. The concrete foundationstructure 52 shown in FIG. 5 is embedded in the ground and has anelongated shape in the depth (vertical) direction.

The concrete foundation structure 52 shown in FIG. 5 is a pre-stressedconcrete foundation structure in which pre-stress is introduced in thevertical direction. Power transmission tower foundations haveconventionally and frequently employed rebar-reinforced concretestructures. However, a pre-stressed concrete structure may be employedwith the view to an improvement in the performance and/or functionality.

The foundation base plate 55 of the concrete foundation structure 52shown in FIG. 5 corresponds to the above-described bearing plate, notincluding separate bearing plates provided correspondingly for therespective tendons but including a single thickened bearing plate usedin common with the multiple tendons. The foundation base plate 55 playsanother role. That is, a power transmission tower foundation truss (acolumnar pipe or an angle bar, for example, is used) is welded onto thefoundation base plate 55 via a reinforcement plate such as a shear plate(not shown). Since the power transmission tower is applied with a groupof loads including its own dead load, wind load, earthquake load, etc.that acts on the wires and/or the tower, it is necessary to transmitsuch an external force to the concrete foundation structure built in theground to thereby maintain the stability of the foundation with areaction force from the ground. That is, a strong cross-sectional forcesuch as a horizontal shear force, a pull-out force, and a bending momentacts on the foundation base plate that is installed on the concretefoundation through the tower foundation truss.

As a method for anchoring a steel truss tower to a concrete foundation,there has conventionally been employed a construction type in which ananchor-shaped steel truss reinforced with a shear plate at the leadingend of the steel truss tower is embedded directly into a cast-in-placeconcrete foundation and reinforced therearound with reinforcing steelbars to integrate the tower foundation truss and the concretefoundation.

In the related-art anchor foundation type, since the anchor portion isinstalled in an inclined manner into the concrete foundation, it is verydifficult to ensure accuracy for the installation. It is particularlynecessary to install the steel truss tower not vertically but in aninclined manner and further at an installation accuracy of as high as 3to 5 mm. This suffers from some problems that a specialized installationtechnique that only a limited number of construction vendors can supportis required and that it results in an increase in the installation cost.

The foundation base plate 55 shown in FIG. 5 has a structure installedhorizontally and directly on the upper surface of the concretefoundation structure 52 and directly utilizing tensioning forces withinthe tendons 51 to resist various active loads from the upper part of thepower transmission tower. The power transmission tower truss isfabricated in a manner inclined with respect to the foundation baseplate 55. A tensile force, a shear force, and a bending moment then acton the foundation base plate 55 as a major cross-sectional force.

A working procedure for introducing pre-stress into the concretefoundation structure 52 shown in FIG. 5 will be described in sequenceand also the synergy with the present invention.

The fixing end portion of each of the tendons 51 will first bedescribed. In the concrete foundation 52 shown in FIG. 5, the fixing endof the tendon 51 is not fixed by a fixing device. That is, the insertionhole (sheath tube) through which the tendon 51 is inserted is not formedentirely from one end (upper end) to the other end (bottom end) of theconcrete foundation 52, but formed to a middle portion of the concretefoundation 52. This is for the reason that since the bottom surface ofthe concrete foundation 52 shown in FIG. 5 is in contact with thesupporting ground, even if the sheath tube may be inserted to the bottomsurface of the concrete foundation 52, there is no space or workingspace to anchor the tendon 51 to the concrete foundation 52 using afixing device.

There has been an untwisting-type anchorage (Japanese Patent No.6442104) practiced as a structure for anchoring one end (fixing end) ofa tendon 51 within a sheath tube (insertion hole) provided in a concretefoundation 52. The untwisting-type anchorage 53 is obtained byuntwisting the twisted side strands (loosening the twisted side strands)that form the tendon 51 along a predetermined length and filling theclearance gap (space) formed thereby with resin mortar or cement mortar.The tendon 51 is inserted through the untwisting-type anchorage 53formed at one end into the sheath tube provided in the concretefoundation structure 52. Before tensioning of the tendon 51, PC grout 56fills the space around the untwisting-type anchorage 53 to thereafter becured. With strength expression in the PC grout 56, the one end portion(fixing end) of the tendon 51 is anchored (fixed) reliably to theconcrete foundation 52.

Before the tendon 51 is inserted into the sheath tube, the foundationbase plate 55 is installed. The foundation base plate 55 plays a role asa bearing plate as well as of fixing the tower foundation truss totransmit a cross-sectional force acting on the tower foundation truss tothe concrete foundation. That is, a shear force and a pull-out force acton the foundation base plate 55.

The tendon 51 is applied with upward tension using a tensioning devicedescribed with reference to FIG. 4. After tensioning operations for allthe tendons 51, PC grout (not shown) fills the sheath tubes and thesleeves 57 to thereafter be cured. After strength expression in the PCgrout, the tensioning forces are released. As mentioned above, since thesleeves 57 are anchored reliably to the tendons 51, the tensioningforces are transmitted through the locknuts 58 engaged with the sleeves57 to the foundation base plate 55, whereby the foundation base plate 55is urged against the upper surface of the concrete foundation 52 andthus pre-stress is introduced into the entire concrete foundation 52. Inaddition, predetermined compression stress occurs in the PC groutfilling the clearance gap between the tendons 51 and the sleeves 57, andthe compression stress causes the tendons 51 to be anchored reliably tothe sleeves 57.

The present invention being applied, the concrete foundation 52 shown inFIG. 5 can show a more critical synergy. As mentioned above, a shearforce and a pull-out force act on the foundation base plate 55. First,if the acting drawing force is weaker than the sum of the tensioningforces, the foundation base plate 55 cannot be deformed upward accordingto the principle of pre-stress. It is therefore only required to set adesign tensioning force greater than the maximum pull-out force.

Next is a resistance mechanism of the foundation base plate 55 by ashear force. Since compression stress due to the tensioning forces actsbetween the foundation base plate 55 and the upper surface of theconcrete foundation 52, the product of the compression stress and thefriction coefficient therebetween serves as a shear resistance. Further,in a method for increase in the shear resistance, convex portions suchas, for example, round steels protrude from the lower surface of thefoundation base plate 55 as shear keys 59, while recessed portions areprovided in the upper surface of the receiving concrete foundation 52,such that the convex portions and the recessed portions are engaged witheach other. This allows the sum of (the cross-sectional area of eachconvex portion)×(the shear resistance stress of each convex portion) tobe considered as shear resistance (design resistance).

It is noted that before installation of the foundation base plate 55,filler/curing agent such as epoxy resin or grout mortar may be put inthe recessed portions so that the convex portions and the recessedportions are in constant contact with each other.

THIRD EXAMPLE

FIG. 6 shows a case where an example according to the present inventionis applied a PC composite bridge. The PC composite bridge is apre-stressed concrete bridge constructed by fabricating a main girderportion and a floor slab portion forming the pre-stressed concretebridge separately on site or in a PC factory and, in a working field,first installing the main girder portion and thereon the floor slabportion and then joining the main girder portion and the floor slabportion.

Referring to FIG. 6, the PC composite bridge shown in FIG. 6 includes anI-shaped main girder portion 63 and a floor slab portion 66 fixed on theupper surface of the main girder portion 63. It is noted that the maingirder portion 63 may have not only an I shape but also a U shape, toboth of which the technique according to the present invention isapplicable. A tendon can be used for (1) joint between the main girderportion 63 and the floor slab portion 66, (2) shear reinforcement byvertical tensioning of the main girder portion 63, and (3) a shearreinforcement bar of the main girder portion 63.

The main girder portion 63 includes a web 63A extending straight-forwardvertically, a head portion 63B formed integrally with the upper surfaceof the web 63A, and a leg portion 63C formed integrally with the lowersurface of the web 63A. A sheath tube (not shown) is provided in the web63A and the head portion 63B, and a vertically extending insertion holeis ensured by the sheath tube. On the other hand, the sheath tube(insertion hole) is provided to a middle portion of the leg portion 63C.

A box-shaped portion (recessed portion) 60 is formed in the uppersurface of the floor slab portion 66, and a bearing plate 69 with athrough hole opened therein is installed on the bottom surface of thebox-shaped portion 60. The sheath tube is inserted from the bearingplate 69 to the lower surface of the floor slab portion 66 to ensure aninsertion hole.

After multiple main girder portions 63 are provided with spacingtherebetween, a vent (temporary bridge pier) (not shown) is providedbetween adjacent ones of the main girder portions 63. After the multiplemain girder portions 63 and the multiple vents are joined and appliedwith tension in the bridge axial direction, the floor slab portions 66are installed. Upon installation of the floor slab portion 66, sealingmaterials 64A are provided on either side of the upper surface of themain girder portion 63 and non-shrink mortar 64B is placed between thesealing materials 64A, onto which the floor slab portion 66 is installed(wet-joint construction method). A tendon 61 with a sleeve 67 and alocknut 68 provided in one end portion thereof and a factory-processeduntwisting-type anchorage 62 provided at the other end thereof isinserted through the box-shaped portion 60 of the floor slab portion 66into the sheath tube of the main girder portion 63. The untwisting-typeanchorage 62 at the other end of the tendon 61 reaches the leg portion63C of the main girder portion 63. Before tensioning of the tendon 61,PC grout 65 fills the space around the untwisting-type anchorage 62.With strength expression in the PC grout 65, the other end portion(fixing end) of the tendon 61 is fixed reliably to the main girderportion 63, as described with reference to FIG. 5. Thereafter, with thesame construction method as that described with reference to FIG. 5, thetendon 61 is applied with upward tension using a tensioning device. Withthe tendon 61 in a tensioned state, PC grout fills the sheath tube andthe sleeve 67 to thereafter be cured. After strength expression in thePC grout, the tension within the tendon 61 is released. Predeterminedcompression stress occurs in the PC grout filling the clearance gapbetween the tendon 61 and the sleeve 67, and the compression stresscauses the tendon 61 to be anchored reliably to the sleeve 67. Inaddition, tensioning load is transmitted to the locknut 68 and thebearing plate 69, whereby pre-stress is introduced into the floor slabportion 66 and the main girder portion 63.

In this third example, synergies with the present invention are asfollows.

(1) First Synergy

In this third example, pre-stress is required to be distributed in thewet-joint portions 64A, 64B between the floor slab portion 66 and theupper end portion of the main girder portion 63. In the presentinvention, since the bearing plate 69 has an effect of distributing atensioning force, required pre-stress can be looked for in the wet-jointportions 64A, 64B. In addition, since the bearing plate 69 can achieve asignificantly small-sized structure compared to related-art tensioningend portions, anchoring jigs can be accommodated within the floor slabportion 66.

(2) Second Synergy

The tendon 61 within the main girder portion 63 contributes to the jointbetween the main girder portion 63 and the floor slab portion 66.Further, the tendon 61 is arranged vertically along the web 63A, withthe ends thereof being anchored to the concrete (the floor slab portion66 and the main girder portion 63), to effectively serve as a shearreinforcement bar. In general, shear reinforcement bars aredisadvantageous in that a bending hook or the like is required forconcrete anchoring to result in a need for additional processing costand/or extra length for anchoring, that is, additional material cost. Inthis third example, shear reinforcement can be provided only with thestraight portion of the tendon 61, leading to cost reduction.

(3) Third Synergy

There are three methods for shear reinforcement of the main girderportion 63: (i) arranging a shear reinforcement bar, (ii) applyingtension to the main girder portion 63 in the bridge axial direction, and(iii) applying vertical tension to the main girder portion 63. Amongthese methods, (i) method of arranging a shear reinforcement bar is mostfrequently employed due to its working easiness and the like. (ii)Method of applying tension in the bridge axial direction is the secondmost-employed one. In a pre-stressed concrete bridge, tension isnaturally applied in the bridge axial direction and thereby a shearreinforcement effect can necessarily be expected. (iii) Shearreinforcement method of applying vertical tension to the web 63A ishardly employed for the reason that it has working difficulty. However,in this third example, the vertical tensioning effect that is applied tothe joint between the main girder portion 63 and the floor slab portion66 can be taken into design consideration as a shear reinforcementeffect of the main girder portion 63. The vertical tensioning effect cansignificantly increase load capacity against shear force and/oroccurrence of oblique crack as well as reduce the width of obliquecrack.

FOURTH EXAMPLE

FIGS. 7 to 10 show processes of manufacturing a pre-stressed concretestructure member using a pre-tensioning system. FIGS. 7 to 9 showlayouts in a side view of a PC production line in a PC factory formanufacturing a pre-stressed concrete structure member. FIG. 10 is apartially broken plan view showing an enlarged version of one endportion of the concrete structure member shown in FIG. 8.

In a general PC production line using a pre-tensioning system, anabutment for taking a reaction force of a tensioning force is providedand the tensioning force undergo fixing anchoring and tension anchoring,respectively, on the fixing side and the tensioning side to manufacturea PC concrete member using a pre-tensioning system. The fixing anchoringand the tension anchoring are here conventionally implemented and willnot be described herein.

In a general pre-tensioning system, such a locknut-and-bearing-plate 75and a sleeve 73 as shown in FIGS. 7 to 9 do not be provided in a memberend portion. Accordingly, upon releasing a tensioning force in a memberend portion, out-of-adhesion may occur between the tendon 71 and theconcrete to result in that (i) if the tendon 71 is a PC steel strand(the diameter of the PC steel strand is represented by φ), it isimpossible to expect pre-stress introduction from the end portion to thepoint of 65φ and (ii) if the tendon 71 is a continuous fiber-reinforcedpolymer strand (the diameter of the continuous fiber-reinforced polymerstrand is represented by φ), it is difficult to expect pre-stressintroduction from the end portion to the point of 50φ.

The example of manufacturing a pre-stressed concrete structure memberusing a pre-tensioning system shown in FIGS. 7 to 9 is directed to thecase where the member has a relatively small length. This is for thereason that since as described above, presetting thelocknut-and-bearing-plate 75 and the sleeve 73 according to the presentinvention allows pre-stress to occur in the member end portion,effective pre-stress can be expected over the entire length of themember even if the member may be relatively short.

A working method according of a fourth example will be described.Basically, multiple (three in FIGS. 7 to 9) formworks 70 are arranged inline with spacing therebetween on a base, and a set oflocknut-and-bearing-plate 75 and sleeve 73 engaged therewith is arrangedin a manner contacting closely to each of the lateral end portionswithin each formwork 70. The tendon 71 is inserted so as to penetrateall the three formworks 70. The tendon 71 is inserted through the hollowspaces of all the sleeves 73 and the through holes of all thelocknut-and-bearing-plates 75 that are arranged in lateral end portionswithin the formworks 70. It goes without saying that holes through whichthe tendon is inserted are opened in lateral end portions within theformworks 70. It is noted that the sleeve 73 is formed with a PC groutfilling port and an air discharge port as will be described below.

Referring to FIG. 7, a tensioning abutment 76 and a tensioning jack 78are provided at one end (tensioning end) (right part in FIG. 7) of thetendon 71 put on the outside of one of the three formworks 70 located atone end (right end in FIG. 7). Also, a fixing abutment 77 and a fixingdevice 79 are provided at the other end (fixing end) (left part in FIG.7) of the tendon 71 put on the outside of one of the three formworks 70located at the other end (left end in FIG. 7). With the other end beingfixed by the fixing device 79, when the one end of the tendon 71 ispulled by the tensioning jack 78, a predetermined tensioning force isintroduced into the tendon 71.

Referring to FIG. 10, a PC grout filling port 73 a and an air dischargeport 73 b are opened in the sleeve 73. PC grout (not shown) fills thesleeve 73 through the PC grout filling port 73 a and air within thesleeve 73 is discharged through the air discharge port 73 b. This causesthe PC grout to fill the clearance gap between the sleeve 73 and thetendon 71 inserted through the sleeve 73.

Referring to FIG. 8, after the PC grout filling the sleeve 73, concrete72 is placed within the formworks 70. The PC grout and the concrete 72are cured until expression of a predetermined strength.

Referring to FIG. 9, after the PC grout and the concrete 72 reaching apredetermined strength, the tendon 71 is released on either outside ofeach formwork 70. The tensioning force within the tendon 71 is loosened(released) and pre-stress is introduced into the concrete 72 within eachformwork 70. In addition, predetermined compression stress occurs in thePC grout filling the clearance gap between the tendons 71 and thesleeves 73, and the compression stress causes the tendons 71 to beanchored reliably to the sleeves 73. Thereafter, when the formworks 70are removed, a concrete structure (pre-tensioned member) into whichpre-stress is introduced using a pre-tensioning system is completed.

With the foregoing series of operations, even a short member can beintroduced efficiently with tensioning stress equally through the endportions thereof. In fabrication of a general pre-tensioned member,since there is a risk for the occurrence of fracturing cracks in amember end portion, the tendon is unbonded by a length of 20 to 30φ inthe member end portion. Comparatively, in this case, since thelocknut-and-bearing-plates 75 are provided in the end portions, such arisk cannot occur.

Comparison with Existing Techniques(1) Post-tensioning System with Bearing Plate and Expansion MaterialSleeve

Existing techniques suffer from three problems as described above underthe foregoing condition.

(i) Limitation on Tensioning of Lengthy Structure

To address this problem, in the present invention, the expansionmaterial sleeve used for tensioning, which is eventually removed fromthe tensioning end portion of the structure, has an increased lengthand/or multiple expansion material sleeves are provided, and tensioningload by the tensioning jack is changed to get rid of the limitation onthe length of the tendon. That is, in the present invention, sinceanchoring the tendon of the continuous fiber-reinforced polymer strandis eventually completed with the sleeve and the locknut engaged with thesleeve, upon completion, only the locknut of the anchoring portion canprotrude from the tensioning end portion as shown in FIG. 1 or theanchoring portion cannot protrude at all as shown in FIG. 6.

(ii) Protrusion of Tensioning End Portion

In the present invention, the anchorage of the tensioning end portionand/or the fixing end portion can basically fulfill their functionswithin the concrete structure as shown in FIG. 1. In addition, thelocknut can be thinned through creative design. As shown in FIG. 6, abox-shaped portion may be provided so that a component is accommodatedwithin the concrete not to protrude at the end portion.

(iii) Adjustment of Tendon Length

On working site, the length of a tensioning target is sometimes requiredto be changed for various reasons. There are two coping methodsaccording to the present invention.

Method A

The expansion material sleeve is fabricated to have an increased length.Since the ram chair shown in FIG. 4 can be divided into several pieces,the length of the ram chair is adjusted as appropriate, so that thefactory-fabricated expansion material sleeve can be utilized adequately.

Method B

No factory-fabricated expansion material sleeve is used. The tendon ofthe continuous fiber-reinforced polymer strand, when carried into thesite, is cut into a necessary length on site. The method of anchoring ofthe fixing end portion and the tensioning end portion basically employsthe system including a friction sheet, a blade net, and a wedge as shownin FIG. 4. This method allows the anchoring position to be determinedaccording to the on-site working conditions, which makes it possible torespond to a change in the length of the tendon. Even in such a case,applying the present invention allows the tension anchoring position tobe set arbitrarily at the working end face, providing no workinglimitation.

(2) Pre-Tensioning System

Problems concerning the pre-tensioning system are as described above. Toaddress these problems, in the present invention, even a short membercan be introduced with predetermined pre-stress between the end portionsas described above. It is also possible to eliminate a risk of splittingcrack occurrence in a member end portion, which has been a working riskin the case of a related-art pre-tensioning system.

What is claimed is:
 1. A tendon anchorage comprising: a bearing platearranged in an outer end portion of a concrete structure with aninsertion hole formed therein and formed with a through hole connectingto the insertion hole of the concrete structure; a hollow sleeveinserted through the insertion hole of the concrete structure and thethrough hole of the bearing plate, one end portion of the sleeve put onthe outside of the concrete structure; a tendon inserted within thesleeve, one end portion of the tendon fixed to the concrete structureand the other end portion of the tendon put on the outside of theconcrete structure; a locknut engaged with the other end portion of thesleeve, which is put on the outside of the concrete structure, and incontact with the outer surface of the bearing plate; and PC groutfilling the insertion hole and the sleeve, wherein before filling withthe PC grout, the other end portion of the tendon is pulled outward by atensioning device with the one end portion being fixed so that thetendon is applied with tension and, after expression of a predeterminedstrength in the PC grout, the tension is released by the tensioningdevice, and the tendon undergoes a Poisson effect to expand radiallyoutward and compression stress occurs in the PC grout between theexpanding tendon and the sleeve.
 2. The tendon anchorage according toclaim 1, wherein the tendon is a continuous fiber-reinforced polymerstrand.
 3. The tendon anchorage according to claim 1, wherein a hollowsheath tube is embedded in the concrete structure, and the hollow spaceof the sheath tube is used as the insertion hole.
 4. The tendonanchorage according to claim 1, wherein the compression stress poccurring in the PC grout and calculated by the following equation 1 is20 to 60 MPa: p=φ/2×v×(0.7×εu)×(t×E)/(R×R) (Eq.1), where φ, v, εu, R, t,and E represent, respectively, the diameter of the tendon, Poisson'sratio of the tendon, tensile strain with guaranteed ultimate load of thetendon, inner radius of the sleeve, thickness of the sleeve, and elasticcoefficient of the sleeve.
 5. The tendon anchorage according to claim 1,wherein at least one of the inner surface and the outer surface of thesleeve is made concavo-convex.
 6. The tendon anchorage according toclaim 1, wherein the bearing plate arranged in the outer end portion ofthe concrete structure consists of a single continuous plate, not pluralplates.
 7. The tendon anchorage according to claim 1, wherein aplurality of convex shear keys are provided on a surface of the bearingplate opposed to the concrete structure, and recesses that the shearkeys enter are formed in positions corresponding to those of the shearkeys on a surface of the concrete structure opposed to the bearingplate.
 8. A tendon anchorage comprising: a pair oflocknut-and-bearing-plates arranged, respectively, in the end portionswithin a concrete structure and each formed with a through hole; ahollow sleeve engaged with each of the pair oflocknut-and-bearing-plates and connecting to the through holes; a tendoninserted through the through hole of each of thelocknut-and-bearing-plates in the end portions within the concretestructure and the hollow sleeve, the end portions of the tendon put onthe outside of the concrete structure; and PC grout filling the sleeve,wherein before the PC grout filling the sleeve and concrete forming theconcrete structure being placed, with one end portion of the tendonbeing fixed using a fixing device, the other end portion of the tendonis pulled outward by a tensioning device so that the tendon is appliedwith tension and, after expression of a predetermined strength in the PCgrout and the concrete, the tension is released by the tensioningdevice, and the tendon undergoes a Poisson effect to expand radiallyoutward and compression stress occurs in the PC grout between theexpanding tendon and the sleeve.
 9. The tendon anchorage according toclaim 8, wherein the tendon is a continuous fiber-reinforced polymerstrand.
 10. The tendon anchorage according to claim 8, wherein thecompression stress p occurring in the PC grout and calculated by thefollowing equation 1 is 20 to 60 MPa: p=φ/2×v×(0.7×εcu)×(t×E)/(R×R)(Eq.1), where φ, v, εu, R, t, and E represent, respectively, thediameter of the tendon, Poisson's ratio of the tendon, tensile strainwith guaranteed ultimate load of the tendon, inner radius of the sleeve,thickness of the sleeve, and elastic coefficient of the sleeve.
 11. Thetendon anchorage according to claim 8, wherein at least one of the innersurface and the outer surface of the sleeve is made concavo-convex. 12.The tendon anchorage according to claim 8, wherein the sleeve is formedwith a filling hole for the PC grout to fill the sleeve and an airdischarge hole for air to be discharged.
 13. A construction method of apre-stressed concrete structure using a post-tensioning system,comprising: arranging, in an end portion of a concrete structure with aninsertion hole formed therein, a bearing plate with a through holeconnecting to the insertion hole of the concrete structure; engaging alocknut with one end portion of a hollow sleeve; inserting the sleevethrough the through hole of the bearing plate into the insertion hole ofthe concrete structure and placing the locknut engaged with the one endportion of the sleeve on the bearing plate; inserting a tendon into thesleeve; fixing one end portion of the tendon; placing a tensioningdevice in the other end portion of the tendon; with the tendon beingapplied with tension, filling the insertion hole of the concretestructure with PC grout such that the PC grout also fills the clearancegap between the sleeve and the tendon inserted into the sleeve; andafter the PC grout reaching a predetermined strength, releasing thetension within the tendon.
 14. A construction method of a pre-stressedconcrete structure using a pre-tensioning system, comprising: providinga formwork; installing, in each lateral end portion within the formwork,a hollow sleeve and a locknut-and-bearing-plate engaged with the sleevesuch that the locknut-and-bearing-plate comes into contact with eachlateral end portion within the formwork; inserting a tendon throughinstallation holes formed in the lateral end portions of the formworkinto the formwork and putting the end portions of the tendon out throughthe respective lateral end portions of the formwork, while within theformwork, inserting the tendon into the sleeve installed in each lateralend portion within the formwork; placing a fixing device in one endportion of the tendon put out of the formwork through one lateral endportion of the formwork; placing a tensioning device in the other endportion of the tendon put out of the formwork through the other lateralend portion of the formwork; applying the other end portion of thetendon with tension using the tensioning device; with the tendon beingapplied with the tension, filling the sleeve in each lateral end portionwithin the formwork with PC grout; placing concrete within the formwork;and after the PC grout and the concrete reaching a predeterminedstrength, releasing the tension within the tendon.